University of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201Some bi-Hamiltonian Systems and their Separation of Variables on 4-dimensional Real Lie Groups8910523941910.22130/scma.2020.122380.764ENGhorbanali -HaghighatdoostDepartment of Mathematics,Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran.SalahaddinAbdolhadi-ZangakaniDepartment of Mathematics, University of Bonab, Tabriz, Iran.RasoulMahjoubi-BahmanDepartment of Mathematics, University of Bonab, Tabriz, Iran.Journal Article20200229In this work, we discuss bi-Hamiltonian structures on a family of integrable systems on 4-dimensional real Lie groups. By constructing the corresponding control matrix for this family of bi-Hamiltonian structures, we obtain an explicit process for finding the variables of separation and the separated relations in detail.https://scma.maragheh.ac.ir/article_239419_91691df474e29d99e062adb4b80f44ae.pdf